We have developed and applied the backprojection-filtration (BPF) algorithm for exact image reconstruction within regions of interest (ROIs) from data containing both longitudinal and transverse truncations. An arc-line scanning trajectory is assumed for the data acquisition. Through the numerical simulation studies, we have shown that with a proper positioning of the patient, even if the patient sizes are larger than the FOV of the scanner, 3D images within the regions of the lung or the heart can be reconstructed exactly from data containing longitudinal and transverse truncations